Power quality basics: Four-quadrant counted energy!

Power quality guide

Four-quadrant counted energy!

Effects, measurements, analysis » Energy flow! » RES installations! » Generation/ recuperation! » Why?

What the four-quadrant energies really are?

Measurements of voltages and currents are the basic possibility to analyze the phenomena occurring in an electrical installation. It is primarily about changes in instantaneous values observed as waveforms, their RMS values representing the energy properties of these signals, as well as power parameters of associated voltage and current pairs - representing instantaneous energy flows. However, in order to be able to determine the balance of these flows, it is necessary to accumulate the results of individual flows, which is done in the counters of energy meters. The matter would be simple and obvious, if not for a few seemingly minor issues related to the fact that energy is an expensive commodity, and the registration of its flow between the supplier and the recipient should be unambiguous.

Since the active power P and reactive power Q have a sign indicating in which direction the individual energies are currently flowing, only one of the four energy states shown in Fig. 1 can occur at any time. The resultant apparent power S can be in the area of one of the four quarters circles, also known as quadrants, as illustrated in Fig. 1. Dividing the circle area vertically, on the right side indicates active power consumption P>0 (green vector). The area on the left side of the vertical axis indicates active power delivery P<0, that is, generation. For each of the two directions (signs) of active power, we can, depending on the sign of reactive power, further divide the individual halves into quarters. The quadrant Q>0 (violet vector) represents the inductive reactive power during active power consumption (P> 0). Then the resultant vector of apparent power S (brown vector) is in the quadrant I. By analogy to active power, it has been widely accepted to distinguish the directions of reactive energy flow depending on the sign of reactive power. On this principle, appropriate counters count individual flows depending on the direction and nature of the power.

Fig. 1. Four-quadrant energies

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Historically, inductive active energy meters used a simple mechanism to make the energy meter rotate only in one direction, counting energy flows in one direction only.

Therefore, in order to determine the consumption and generation of active energy, it was enough to use two meters simultaneously. The same was done with reactive energy during consumption, for which the energy recipient was responsible for settlements. It was enough to install two additional meters at the consumption: one for inductive reactive energy, and the other for capacitive reactive energy. Currently, energy flows are unambiguously measured in integrated electronic energy meters with counters for all possible flow states. However, there are also simplified solutions that use the previously mentioned unjustified convention for determining the directions of reactive power flows, as shown in Fig. 2. Since this solution is still quite common, even in advanced electronic analyzers, it will also be described briefly for the sake of explanation. For the power Q>0, there is one reactive energy index marked EQ+, called the reactive energy, and for the power Q<0, one index marked with EQ-, called the returned (generated) reactive energy. You can see immediately that the adopted convention is ambiguous, because one passive abacus counts for two directions of active energy flow, so it is not Fig. 2. Simplified analysis of energy flows clear what the EQ+ and EQ- abacuses represent. The only case in which the uniqueness of the simplified method is preserved is the status of only active energy consumption, then EP- = 0, or only generation, when EP+ = 0. Because it is more and more difficult to find such unambiguous cases in power networks, the simplified solution will not always be effective and therefore it should be paid special attention when selecting measuring equipment for specific applications.

This limitation is not present in a fully four-quadrant meter. To ensure the unambiguous ability of the meter to distinguish all cases, the counting must take place in individual areas represented by quarters of a circle (Fig. 3), with the separation of pairs of reactive energy counters for active energy consumption and for generation. This creates a total of 6 energy counters unambiguously associated in pairs with individual quadrants of the circle area (quadrants).

The importance of a full four-quadrant analysis is all the greater that in some countries, regulations define the quality of energy, provided that the tg (φ) factor and maximum power (e.g. 15 or 30 minutes) are met. Only having unambiguous flows of inductive reactive energy during active energy consumption, it is possible to clearly determine the appropriate parameters.

There remains the last problem in the four-quadrant analysis of energy flows. It applies to networks with both unbalanced load and unbalanced energy generation. Such cases are becoming more and more common in the face of rapidly spreading renewable energy and prosumer photovoltaic installations. It turns out that the four-quadrant analyzes valid for phase powers have a physical sense, but the analysis of the three-phase balance of reactive energy, calculated using the vector method, may give ambiguous results for three-phase flows.

Fig. 3. Full, four-quadrant analysis of energy flows

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Three examples of improper energy results!

Example I The example for a RES facility presented in Fig. 4 contains the following inaccuracies due to the wrong selection of the analyzer, which did not have 4-quadrant meters: a.) The maximum 15-min power was determined on the basis of the average active power, which could result in an underestimated value caused by the simultaneous occurrence of consumption P>0 and generation P<0, affecting one value of average power within 15 minutes, b.) A very high value of the tg(φ) coefficient caused by the occurrence of the mean active power close to 0 in the transitional moments, which as a result of dividing Q>0 by P≈0 gave the results of the tg(φ) coefficient, which was mathematically correct, but had no practical significance.

It was caused by the incomplete quadrant analysis algorithm, and the only solution to this problem is to use full four-quadrant recording and analysis of energy flows, and to determine the value of tg(φ) based on the total energy flow during consumption.

a.)

b.)

Fig. 4. Analysis of tg(φ) conditions and maximum 15-minute average power

The solution to this problem is very simple - in the case of renewable energy installations, micro renewable energy sources or installations enabling temporary energy recovery, it is enough to use analyzers enabling full four-quadrant analysis with updating the counters every 10 network periods, e.g. SONEL class A: PQM-702/703/710/711. The use of typical and common power parameters analyzers, without full and fast four-quadrant analysis, is possible only for diagnostic purposes, provided that power direction changes occur much slower than the applied averaging time. However, this requires additional attention, larger data file sizes and may not always be fully effective in special cases.

Example II The problem occurs especially with the increasingly popular devices with optimized energy consumption. Using typical averaging times of the order of 10 s in the case where devices are able to briefly recover energy and return it to the grid, a typical reactive power analysis based on average powers, or even energy counters with incomplete quadrant analysis, will result in erroneous conclusions. Similarly, when the nature of reactive power as a result of load disturbance will change many times during one averaging period. Then, the average active and reactive powers determined by the algorithms and the typically calculated energy flows at the end of the averaging period will be false. The solution to this problem is a full, four-quadrant energy meter updated every 10 network periods, as is the case with PQM analyzers.

Example III It is associated with the more and more common micro renewable energy. Fig. 5 shows the average three-phase active power (red) and the average three-phase generated active power (green).

For the sake of clarity, the figure shows only the average power consumed in each phase. The area a.) Shows the average active power P+ 15min Σaverage=0 despite the fact that the visible phase powers are consumed (P>0). In area b.) Three-phase powers, both consumed (red) and generated (green), are already visible as P<>0. The three-phase power quantization algorithm according to the vector balance caused the calculation of three-phase energies only when the three-phase powers are different from 0. As a result, the dominant generation power masked the share of non-zero input phase powers in the area a), as a result of which the observed three-phase image is ambiguous.

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a.) b.)

Fig. 5. The image of three-phase average active powers broken down into consumed (red) and generated (green)

A few simple steps to perform diagnostics and energy measurement The most important thing is to reliably register energy. With the PQM-701xx analyzer, it is possible to register cases of active and reactive energy flows for unambiguous loads or unambiguous generations (without the occurrence of consumption states). For generation and consumption, the class S analyzers (PQM-700, PQM-707) or class A analyzers (PQM-702/703/710/711) should be used. In order to unambiguously register energy flows: 1. In the recording settings, in the Powers and energies tab, enable recording in accordance with IEEE 1459 and recording of active powers P and reactive powers Q1.

2. In the energies tab, enable recording of all energies.

3. After connecting to the analyzer, send the modified settings.

Fig. 6. Energy recording settings

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4. Register the selected moment of work of the object using the START/STOP function.

5. Read the results with the Sonel Analysis software.

Analysis of energy measurement results After reading the measurement file containing energy recording with the Sonel Analysis software, you should: 1. Press the Measurements button.

2. Find on the list the interesting average powers or quadrant tangents.

3. You can enlarge interesting parts of the measurement by changing the time scale and the vertical scale.

4. By placing markers 1, 2, 3 in characteristic places (Fig. 5), read the moment and the parameter value for each of the three markers depicted with a circle icon with a number.

5. On the basis of the results of the differences from the markers, the time interval and values between individual points of the same signal can be determined.

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